Gravity’s immunity from vacuum: the holographic structure of semiclassical action

Principle of equivalence, general covariance and the demand that the variation of the action functional should be well defined, lead to a generic Lagrangian for semiclassical gravity of the form L = Q bcd a Rbcd with ∇b Q bcd a = 0. The expansion of Q bcd a in terms of the derivatives of the metric tensor determines the structure of the theory uniquely. The zeroth order term gives the Einstein–Hilbert action and the first order correction is given by the Gauss–Bonnet action. Remarkably, any such Lagrangian can be decomposed into a surface and bulk terms which are related holographically. The equations of motion can be obtained purely from a surface term in the gravity sector and hence gravity does not respond to the changes in the bulk vacuum energy density. 1 Gravity: kinematics versus dynamics The elegance of general relativistic description of gravity rests on the geometric structure, which – in turn – is based on the principle of equivalence (PE). In its simplest form, PE allows the description of gravity in terms of a metric tensor and determines the kinematics of gravity (‘how gravity tells matter to move’) by invoking special relativity in the local inertial frames. Contrast this with the description of dynamics of gravity (‘how matter tells spacetime to curve’) for which we completely lack a similar guiding principle. Classical dynamics has to arise from semiclassical limit of quantum gravity Third award in the 2006 Essay Competition of the Gravity Research Foundation. T. Padmanabhan (B) IUCAA, Pune University Campus, Ganeshkhind, Pune 411 007, India e-mail: [email protected]